How to make an interactive two-finger robot gripper and grab things with it?
Instead of Softbody physics, consider Rigid Body physics for the robot parts (this will keep them from jiggling when they interact with something; that is, they'll interact, but they won'd deform their own shape, which is what you want). Rigging is actually extremely simple for hard surface models like this, and your best option for what you want to achieve. You don't have to automatically weight the bones, either, which might not give the desired results in this case, since it likes to use falloff (good for organics, not so much for robots).

What you'll want to do first is set up your bones so they lay inside your model, with the joints where you want the bending to happen. Now you'll want to head over to the bone tab, found in the section of the workspace where you usually go for your physics stuff. It should look like a little bone. Click this, and you can change a few things to make your life easier. Mainly, X-ray. It should be on by default, but if it isn't, this is where you'll find it. Also playing with contraints is useful, if you don't want to fool with with exact degrees of rotation while you're manually moving your bones. Adding a contraint limited to the range of motion of your grippers will physically prevent you from moving the bone too far, so you're freer to eyeball it. Just a few more steps, and you'll be on your way! Hide your armature via the outliner window for now, or move it to another layer. We need to work on the robot itself. All you need to do is make vertex groups for each rigid piece. (Each piece should have it's own corresponding bone.) Once you have them named, bring your armature back (your collection of bones) and rename the bones to match the vertex group they're supposed to control. When you finish, select your mesh, then your armature, and parent them.